Advocates of a balanced-budget amendment to the Constitution, taking advantage of rising concern over deficits and frustration with congressional delays, expect to win state approval early next year for the first U.S. constitutional convention in two centuries.

A nine-year-old campaign by the National Taxpayers Union (NTU) and other groups has secured resolutions from 32 state legislatures directing Congress to call a convention to consider a balanced-budget amendment. Only two more states are needed to force congressional action, and proponents of the amendment said this week that they expect favorable responses from Michigan and Montana by early November, although the Montana process would take until early next year to complete.

"We are closer than we have ever been before," said NTU executive vice president David Keating, who flew to California Tuesday to help a stalled amendment campaign in that state. "The next five to seven months are going to be crucial."

Michigan state Rep. Jerry Bartnik, a Democrat who has become a key swing vote on the amendment in his state, said: "I have groups coming out from Washington to see me that I've never heard of before."

Opponents of the balanced-budget amendment have bottled up amendment bills in Congress. They also succeeded Monday in winning a California state Supreme Court ruling that a balanced-budget initiative on the November ballot is unconstitutional.

But amendment supporters in other states say they will not need California to put the proposal over the top. On Sept. 13, a committee of the Michigan House of Representatives is expected to send a request for a constitutional convention, already approved by the state Senate, to the House floor. A balanced-budget initiative on Montana's November ballot has received 74 percent support in one poll and so far has escaped constitutional challenge.

The AFL-CIO and other labor and civil rights groups have argued that constitutional limits to government spending would kill Washington's ability to fight a recession. They say the amendment would hurt poor and disadvantaged groups that depend on federal support.

Proponents say the amendment is the only way to force members of Congress to stand up to special interests that demand more spending than the government can afford. Record federal deficits have shown the urgency of this approach, they say, and President Reagan has endorsed the amendment and a presidential line-item veto as the best solutions to the deficit problem.

The Senate Judiciary Committee approved without dissent on May 17 the Constitutional Convention Implementation Act of 1984. The act would require the popular election of delegates to any new constitutional convention -- one from each congressional district and two from each state.

The act also would prohibit any convention from straying beyond the issue it was called to consider. Supporters of the balanced-budget amendment argue that any other amendments the delegates might try to pass would be struck down by the courts or fail to win approval of 38 states -- the number required under Article V of the Constitution for ratification of any amendment that might come out of a constitutional convention.

Constitutional scholar Gerald Gunther, a Stanford University law professor, said this week that most scholars still think a runaway convention is possible. He noted that Article V refers to amendments in the plural, saying, "Congress, . . . on the application of the legislatures of two-thirds of the several states, shall call a convention for proposing amendments . . . ."

With so many other constitutional issues such as abortion and school busing being discussed, he said "it is still an open question" whether delegates would have to limit themselves to one and whether courts could do anything to stop them.

"The only way to stop it would be political," in the popular voting for delegates and the later votes on ratification in the state legislatures, said Steve Silbiger, associate director for legislation for the American Federation of State, County and Municipal Employes.

Keating, who estimates that the NTU and other groups have spent $2 million to $5 million campaigning for the amendment, was in Sacramento this week, helping with an effort to reintroduce the amendment on the floor of the California Senate. Californians to Balance the Budget, which collected 605,000 signatures to put the proposal on the ballot, has asked U.S. Supreme Court Justice William H. Rehnquist to stay the state high court decision eliminating what would have been Proposition 35. A decision is not expected before early next week.

In Montana, a similar initiative remains on the ballot. Cliff Christian, director of the Helena-based Political Education Council of Montana, said supporters have raised about $50,000 for radio ads and other promotion while opponents have yet to speak out. The initiative would require next year's state legislature to remain in session until it passed a request for a constitutional convention, and would cut off members' pay and benefits if the session ran beyond the 90-day limit.

A similar provision in the California initiative was ruled unconstitutional by the state Supreme Court on grounds that legislators would not be "free to vote their best judgment." Montana opponents are preparing a political and legal campaign against the initiative, but may wait to see if it passes before challenging it in court.

In Michigan, the constitutional revision and women's rights committee of the state House of Representatives is scheduled to consider a constitutional convention for the balanced-budget amendment Sept. 13. The committee's four Republicans support the amendment and four of its five Democrats appear to be opposed, leaving the remaining Democrat, Bartnik, the focus of much attention.

Facing a difficult reelection campaign in a district that is only 51 percent Democratic, Bartnik first leaned toward the amendment until he heard some advocates say publicly that new taxes might be needed to balance the budget.

Michigan has been torn by anti-tax fervor. Two Democratic state senators were recalled and replaced with Republicans after they voted to raise state taxes. This helped win a 23-to-15 Senate victory for the balanced-budget-amendment resolution in April, but Bartnik said talk of the amendment's forcing tax increases scares him.

Jack Mowat, a former Michigan legislator helping to direct the House GOP staff, said a vote in the House would be close, "but I think it could pass." Dennis Schornack, legislative assistant to the Senate majority leader, was less certain. He noted that the House has a 63-to-46 Democratic majority and is led by amendment opponents.

Balanced-budget activists also say the amendment may pass next year in Ohio and Washington. Ohio state Rep. Michael Fox is leading an effort to collect 335,673 signatures for a 1985 ballot initiative.

Jim Medley of Washington Citizens for a Balanced Budget said his group fell 8,000 signatures short of the required 138,000 for a ballot initiative in his state. But he said both houses of the state legislature have passed some version of a balanced-budget resolution in the past. With urging from businessmen, he said, both houses might agree on a resolution next year.